Estimating Tennis In-Match-Win Probability with Bayesian Modeling

Introduction

Bayesian Prior, Data, and Posterior

Johnson, A. A., Ott, M. Q., & Dogucu, M. (2021). Bayes Rules! An Introduction to Applied Bayesian Modeling

Prior Distribution

Prior Distribution

Data + Posterior

Data + Posterior

Calculating In-Match-Win Probability

Match-Win Probability vs Winning-Point Probability (on Serve)

Case Study 1: Alcaraz vs Sinner

• In the 2022 US Open, Carlos Alcaraz faced Jannik Sinner in the quarterfinals
• Alcaraz defeated Sinner in 5 sets, 6-3, 6-7(7), 6-7(0), 7-5, 6-3
• We will look at probability of Alcaraz winning the match
• Probability of winning a point on serve at the start of the match:
  • \(p_{alcaraz}: 0.6229\)
  • \(p_{sinner}: 0.5606\)

Case Study 1: Alcaraz vs Sinner

Case Study 1: Alcaraz vs Sinner

Case Study 1: Alcaraz vs Sinner

Case Study 1: Alcaraz vs Sinner

Case Study 1: Alcaraz vs Sinner

Case Study 1: Alcaraz vs Sinner

Case Study 1: Alcaraz vs Sinner

Case Study 1: Alcaraz vs Sinner

Case Study 1: Alcaraz vs Sinner

Case Study 1: Alcaraz vs Sinner

Case Study 1: Changing Prior

Case Study 2: Gauff vs Sabalenka

• In the 2023 US Open, Coco Gauff faced Aryna Sabalenka in the finals
• Gauff defeated Sabalenka in 3 sets, 2-6, 6-3, 6-2
• We will look at probability of Gauff winning the match
• Probability of winning a point on serve at the start of the match:
  • \(p_{gauff} : 0.5880\)
  • \(p_{sabalenka} : 0.5475\)

Case Study 2: Gauff vs Sabalenka

Case Study 2: Gauff vs Sabalenka

Case Study 2: Gauff vs Sabalenka

Case Study 2: Gauff vs Sabalenka

Case Study 2: Gauff vs Sabalenka

Case Study 2: Gauff vs Sabalenka

Conclusion

• Dynamic Nature

• Data-driven Insights

• Future Directions

Acknowledgements

• Jeff Sackman Github
• Skoval deuce package
• James Wolpe SLU ’23 prior distribution
• Dr. Matt Higham